In the Middle Eastern traditions which dominate in Europe and America, a religion is a system of beliefs and practices which claims truth and demands loyalty: you cannot simultaneously be two of Christian, Jewish, or Muslim. In Asia, at least until fairly recent European influence, the concept rather was that of ways or paths. Over millennia there was a lot of cross-fertilization among various spiritual practices (which we now call Hindu, Buddhist, Taoist, etc. — “ist” and “ism” are European concepts) and it was possible to move among them without abandoning one for another. For example, in Japan it was common for people to be married by a Shinto priest and buried by a Buddhist one. There is no concept of conversion from one religion to another. You simply practice one way or another or even many at the same time. Why not?
Zen is part of Mahayana Buddhism, so is a religion in the way that all forms of Buddhism are. But it has no belief system one has to adhere to. Buddhist precepts are promises about behavior: not to kill, not to steal, not to lie, and so on — five to start off with, and hundreds if you become a nun or monk. There is no precept about what you believe. Which is why you can find Zen practitioners and even teachers who practice various monotheistic traditions. There are Catholic priests, Protestant ministers, and Jewish rabbis who are Zen masters.
So the answer to your question is: it depends how you define “religion.”